Video Transcript
The current induced in a loop of
wire increases at 0.16 amperes per second. The loop has a self-inductance of
0.55 henrys. What is the potential difference
across the loop?
Let’s say that this is our loop of
wire. The wire carries current, and that
current changes over time at a rate of 0.16 amperes per second. This change in current is due to a
change in the magnetic flux experienced by the loop. The relationship between how much
current changes for a given change in magnetic flux is called the self-inductance of
the loop. Self-inductance is represented
using a capital 𝐿, and the units of self-inductance are henrys. One henry is defined as a weber,
the unit of magnetic flux, per ampere, the unit of current. We see then that inductance really
does relate magnetic flux to current.
In this example, we want to solve
for the potential difference that is induced across the loop. In order for current to be induced
and to exist in the loop, there must be some potential difference induced across
it. That potential difference, which we
will represent in general using this script 𝐸 or letter 𝜀, is equal to the
self-inductance of a loop multiplied by the change in current in that loop divided
by a change in time. We’ve seen that, in our case, Δ𝐼
divided by Δ𝑡 is 0.16 amperes per second and 𝐿 is 0.55 henrys. So then, the potential difference
across our loop of wire equals 0.55 henrys times 0.16 amperes per second, and this
product is equal to 0.088 volts. This is the potential difference
that is induced across the loop.
